Sketch of notation for diagramming sentences

Note that this is an attempt to combine the diagramming graphics with the associated grammatical function information. An alternative approach -- maybe a better one -- would be to focus first on the graphical primitives alone -- branches, standards, etc -- and then worry later about how to translate grammatical information into those graphical forms.

Kinds of relations:

Name: subject of
Relation: binary
-- [e1 e2], e1 is the subject of e2
Function: from subject + VP to sentence?
Graphics: main sequence (~ heads) of e1 e2 above a horizontal line, with a vertical line between them through the horizontal line.
Symbol: subj
Example: Glaciers melt = (subj "Glaciers" "melt")

Name: coordination
Relation: 3-ary -- [e1 e2 e3], e2 and e3 are coordinated with operator e1
Function: from type of e2 and e3 to the same?
Note: not clear how these guys deal with varieties of multiple coordination ('A, B and C' v.s 'A and B and C')
Graphics: main sequences of e2 and e3 are on parallel horizontal lines ("branches"), joined with oblique lines to preceding and/or following sequences as appropriate; operator e1 is along vertical line connecting the two parallels, at the left or right side; joined end is preferred over open end, otherwise left end is preferred over right (??)
Symbol: coord
Example: The professor and her colleagues are studying glaciers and avalanches
(subj (coord "and" (mods "The" "professor") (mods "her" "colleagues")) (dobj "are studying" (coord "and" "glaciers" "avalanches")))
Example: The professor and her colleagues are studying and classifying glaciers(subj (coord "and" (mods "The" "professor") (mods "her" "colleagues")) (dobj (coord "and" "are studying" "classifying") "glaciers"))

Name: indirect object
Type: binary -- [e1 e2], e2 is the indirect object of e1
Graphics: the main sequence of e2 is written on a horizontal line below the main sequence of e1, connected by a right-slanted oblique line.
Symbol: iobj
Example: Professor Higgins gave her students two projects.
(subj "Professor Higging" (dobj (iobj "gave" (mods "her" students")) (mods "two" "projects")))

Name: prepositional phrase(s)
Relation: each PP is basically 3-ary -- [e1 e2 e3], e2 is a preposition, e3 is its object, e1 is what it modifies (??)
Graphics: e3 is written on a horizontal line below the main sequence of e1, connected by a right-slanted oblique line, on which e2 is written.
Symbol: pmods, pp -- pmods is exactly like mods, pp is like mods but binary (see below for usage)
PROBLEM: multiple modifying PPs are treated like other multiple modifiers -- see p. 9 -- not clear how they should interact...
Options would be
1.
to treat PPs as literal modifiers --
"studied in Antarctica during the 1950s" ==
(mods (pp "in" "Antarctica") (pp "during" (mods "the" "1950s")) "studied")
2. to add a special pmod operator to distinguish pp and other modifiers --
"studied in Antarctica during the 1950s" == (pmods (pp "in" "Antarctica") (pp "during" (mods "the" "1950s")) "studied")
3. to curry the PPs --
"studied in Antarctica during the 1950s" == (pp (pp "studied" "in" "Antarctica") "during" (mods "the" "1950s"))
My conclusion: (2) is the most coherent option, though I might change my mind.
Function: pmods is like mods, pp is from P+NP to Modifier?
Example: Professor Higgins studied glaciers in Antarctica during the 1950s.
(subj "Professor Higgins" (dobj (pmods (pp "in" "Antarctica")(pp "during" (mods "the" "1950s")) "studied") "glaciers")